Abstract
In this paper, we consider a stochastic SIRS epidemic model with standard incidence. By constructing suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of ergodic stationary distribution of the model. Moreover, we also establish sufficient conditions for extinction of the disease.
•A stochastic SIRS epidemic model with standard incidence is proposed and studied.•Establish sufficient conditions for the existence of ergodic stationary distribution.•We also establish sufficient conditions for extinction of the disease.